In 1948 C. Shannon, the founder of Information Theory, published a paper that showed that no more thanC=W log 2 (1+SNR)
bits could be transmitted over a digital communications channel without error, where C is called the channel capacity in bits/sec/Hz, W is the channel bandwidth in Hz, and SNR is the signal-to-noise-power ratio. He also proved that codes existed that allowed rates arbitrarily close to C with arbitrarily small error rates.
He did not show how to construct these codes, and none were discovered until Berrou et al. invented turbo codes (C. Berrou, A. Glavieus and P. Thitmayshima, “Near Shannon Limit Error-Correcting Coding and Decoding: Turbo Codes,” Proc. Of 1993 International Conference on Communications, pp. 1064-1070, 1993) that have rates close to C at low SNRs (e.g., 3 db) but not at high SNRs of 15 to 30 db. Turbo codes are now widely used where reliable communication at low SNRs such as NASA deep space channels is required.
Computer hard disk drives are binary channels that typically have strong intersymbol interference (ISI) as a consequence of recording information at as high a density as is possible, and the resulting ISI is countered with Viterbi detectors, as first described in “Error Bounds for Convolutional Codes and an Asymptotically Optimum Decoding Algorithm,” published in IEEE Transactions on Information Theory, Volume IT-13, pages 260-269, in April, 1967. Error correction that is internal to the Viterbi detector has been investigated by several commercial vendors. Strong parity checks or block code decoders such as Reed-Solomon decoders external to the detector are generally used.